Question on the Law of Reflection

[manofslate]

The law of reflection states that the angle of incidence equals the angle of reflection.

In the event of a beam of light reflecting upon a horizontal surface, the incidence angle is 45 degrees (as a variable, 45 degrees will be represented by A).

The angle formed by the reflection will also be 45 degrees (demonstrating the law of reflection).

There is a third angle which has also been formed. If the line is horizontal (by horizontal, I mean that a perceived vertical auxiliary line could be drawn and intersect with the first line to form two right angles), then the total value should 180 degrees.

The values of the angles of reflection and incidence are equal, therefore I’ll refer to them both with the variable A. So, 2A is the value of both angles.

180 -2(45) = 90.

In between the two lines formed by the incidence and reflection of the beam of light, there exists a right angle (this surely must be the case because an additional ninety degrees is necessary to complete 180 degrees.

So, the third angle formed (with respect to the two angles formed by the reflecting beam of light) is summed up by the equation:

2A + X = 180

The variable X will be the remaining angle


Basically, if a reflective surface is horizontal, can this surface be viewable as the diameter of a circle, with a total angle measure of pi radians (180 degrees)?

If this is the case, then the angle in-between the angles formed by incidence and reflection must ensure that the total amount of degrees will equal 180 degrees, am I correct?

Sorry, it’s been a while since I’ve studied the law of reflection, but I’m still curious.

Oh, and forgive me if there are any fallacies. I'm only a sophomore in high school, and I really hastily scrawled this out.

 

[Claude Bile]

Firstly, welcome to the forums!

Your understanding of the law of reflection is correct, except that angles in this context are conventionally taken with respect to the surface normal (not parallel to the surface).

I am also confused by this statement;

Basically, if a reflective surface is horizontal, can this surface be viewable as the diameter of a circle, with a total angle measure of pi radians (180 degrees)?

Claude.

 

[manofslate]

Hey Claude,

Thanks for reading this. I didn't clarify on the aforementioned statement; mixing up on units and such. To make it simple, all of the angles formed by the reflecting light on the given surface are supplementary, correct? They must all total 180 degrees?

 

[Doc Al]

To make it simple, all of the angles formed by the reflecting light on the given surface are supplementary, correct? They must all total 180 degrees?

Only because you've assumed a flat surface. This would be true even if the angles of incidence and reflection were not equal. (Unless I missed your point.)